This invention relates to the field of digital rock physics and specifically to methods to estimate effective atomic number and/or bulk density of rock samples.
Density and effective atomic number measurements of well cores are valuable to reservoir engineers. Bulk densities give an indication of porosity and effective atomic number provides an indication of mineralogy.
There are a number of ways that one can estimate density and effective atomic number including:                1. Physical samples can be withdrawn from the well and density can be measured by weighing the sample, calculating its volume and simply dividing weight by volume.        2. Well logging tools can be used to estimate density and effective atomic number. Gamma-gamma ray techniques are used to estimate density and effective atomic number from the absorption of gamma ray radiation as it passes through the rock in the well bore.        3. X-ray CT scanners can be used to estimate density and effective atomic number by measuring the attenuation of X-rays at two different energy levels and then using the measurements to calculate the density and effective atomic number.        
In the 1970's, X-ray computed tomography scanners (CT scanners) began to be used in medical imaging. In the 1980's, these scanners were applied to rock samples extracted from well bores (cores). CT scanners have the advantage of higher resolution than gamma ray logs and they are not affected by environmental conditions as downhole gamma-gamma ray logs are. In addition, CT scanners produce a 3-D distribution of rock properties in the sample, while the logs provide only a 1-D distribution.
Wellington and Vinegar (Wellington, S. L. and Vinegar, H. J., “X-Ray Computerized Tomography,” JOURNAL OF PETROLEUM TECHNOLOGY, 1987) reviewed the use of CT scanners in geophysics. The attenuation of X-rays depends upon both electron density (bulk density) and effective atomic number.
                    μ        =                  ρ          (                      a            +                                          bZ                3.8                                            E                3.2                                              )                                    (        1        )                            where                    μ is the linear X-ray attenuation coefficient            ρ is the bulk density            Z is the effective atomic number            E is the photoelectric absorption            a and b are constants.                        
The medical CT scanners provide 3-D volumes of CT values, which are in linear relationship with the attenuation coefficient, μ. The first term in equation (1) is significant at high X-ray energy levels (above 100 kv) while the second term is significant at low X-ray energy levels (below 100 kv). A dual energy scan can therefore be used to make estimates of both bulk density and effective atomic number. Considering a dual energy scan, equation (1) leads to the following equations:ρ=A*CThigh+B*CTlow+C  (2)ρZeffa=D*CThigh+E*CTlow+F  (3)                where                    ρ is the object's density,            Zeff is its effective atomic number,            A, B, C, D, E, F are coefficients,            CThigh and CTlow are X-ray CT values of the object obtained at high and low energies of X-ray quanta,            α is approximately 3.8.                        
As indicated, for example, by Siddiqui, A. and Khamees, A. A., “Dual-Energy CT-Scanning Applications in Rock Characterization,” SOCIETY OF PETROLEUM ENGINEERS, 2004, SPE 90520, estimating effective atomic number and bulk density distributions in core samples from dual energy X-ray CT involves:                a) Acquiring X-ray CT image of the target object along with at least three objects (calibration objects) with known density and known effective atomic number. In the case of cores, the core axis is aligned with the Z axis of the image (see FIG. 1).        b) Recording the high/low energy CT values of the calibration objects and the target object and averaging them in each object and/or in each XY section of each object.        c) Using the known properties of the calibration objects and their high/low energy CT values, solve the system of equations (2,3) for coefficients A, B, C, D, E, F.        d) Using the target object's high and low CT values and coefficients from Step c), calculate the target object's density and effective atomic number from equations (2, 3).        e) Calculate the density and effective atomic number logs by averaging the values of density and effective atomic number in each X-Y section of the scan.        
Typically, steps b) and c) are performed for each section of the CT image parallel to the X-ray path (e.g., each X-Y section), and step d) is performed in each point (e.g. voxel) of the 3-D image, using coefficients determined for the corresponding X-Y section.
The problem with this approach is that the model determined by equations (2,3) does not account for all effects involved in the process of X-ray computed tomography. As a result, the density values obtained in step d) and averaged over the target object do not always match the object densities determined by direct physical measurement, mass divided by volume. An example using the traditional method for estimating bulk density and effective atomic number for a shale sample is shown in FIG. 2 and FIGS. 3a-b. 
Calculated densities are mostly less than measured, with the error sometimes exceeding the typically acceptable level of 5%. There is no visible correlation between measured and calculated density values (correlation coefficient=−0.27).
In addition, the relationship between the effective atomic number and bulk density values calculated from dual energy method is very often difficult to explain by accepted rock physics models, which state that the rock density is, in general, increasing with the increase of the effective atomic number. See, for example, FIG. 3a) shows effective atomic number plotted versus bulk density values for a shale sample obtained by direct measurement, and exhibits in general an increase in the density when effective atomic number is increasing. The trend in FIG. 3b), displaying effective atomic number plotted versus calculated averaged bulk density shows an almost opposite trend. This effect was observed by Boyes (Boyes, J., “The Effect of Atomic Number and Mass Density on the Attenuation of X-rays,” QUEEN'S HEALTH SCIENCES JOURNAL, 2003). On the other hand, the errors of effective atomic number are within acceptable limits. An example of a match between effective atomic number obtained from sample's mineral composition and effective atomic number estimated with the dual energy method is shown in FIG. 4.
Accordingly, the previous approaches to estimating density and/or effective atomic number of rock samples or well cores has shown to be not accurate enough to provide suitable information to the drilling and hydrocarbon recovery industry. There is a need for a more accurate method(s) to estimate effective atomic numbers and bulk densities of rock samples. Furthermore, a method for estimating effective atomic number and/or bulk density of rock samples needs to be provided that overcomes one or more of the above-identified problems.